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Minimax Hierarchical Empirical Bayes Estimation in Multivariate Regression

✍ Scribed by Samuel D. Oman

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 171 KB
Volume: 80
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.2000.1985

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✦ Synopsis

The multivariate normal regression model, in which a vector y of responses is to be predicted by a vector x of explanatory variables, is considered. A hierarchical framework is used to express prior information on both x and y. An empirical Bayes estimator is developed which shrinks the maximum likelihood estimator of the matrix of regression coefficients across rows and columns to nontrivial subspaces which reflect both types of prior information. The estimator is shown to be minimax and is applied to a set of chemometrics data for which it reduces the crossvalidated predicted mean squared error of the maximum likelihood estimator by 380.

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